Everything. Moving the viewports, selecting surfaces, placing actors, live preview (all that under both software rendering and OpenGL), selecting textures, playing sounds, editing actor properties, rebuilding levels, the 2D shape editor.
What does not
If you open texture properties and drag your mouse in the texture preview, the mouse gets stuck inside the tiny window. Pressing alt-tab lets it go free, though.
What was not tested
This was just a quick look, so I may have missed something, but I tried to be fairly thorough.
Testing was done using an NVIDIA GTX 660, with proprietary drivers. UnrealEd doesn't strictly need to be installed to work, either, launching an already installed instance on Windows works just fine too.
|Operating system||Test date||Wine version||Installs?||Runs?||Used|
|Current||openSUSE 13.1 x86_64||Aug 26 2014||1.7.25||Yes||Yes||Gold||GreatEmerald|
|Show||openSUSE 11.4 x86_64||Jul 03 2011||1.3.20||N/A||Yes||Bronze||GreatEmerald|
|Show||Ubuntu 9.04 "Jaunty" amd64 (+ variants like Kubuntu)||Oct 22 2009||1.1.31||Yes||Yes||Bronze||Justin Soulia|
|Show||Ubuntu 8.10 "Intrepid" i386 (+ variants like Kubuntu)||Aug 22 2009||1.1.27||Yes||Yes||Bronze||an anonymous user|
|Show||Ubuntu 8.04 "Hardy" i386 (+ variants like Kubuntu)||Oct 04 2008||1.1.5||N/A||Yes||Bronze||Justin Soulia|